ME360: PRODUCT DESIGN
ME360 Product Design is a project-based course completed during my third-year while in undergrad. The following menu presents the sections taught throughout the course, intended to aid in the development of various practical skills. Under each section, you will find a series of design exercises, completed projects, and design analyses.
UNDERSTANDING HOW TO DESIGN
A MOTOR DRIVEN MECHANISM
Assignment #3: Plotter Pen Deployment Mechanism
As designed and written by Isabella R. Reyes
April 9, 2021
MECHANISM DESGIN
ANALYSIS OF MECHANISMS
SYNTHESIS OF MECHANISM
DEGREES OF FREEDOM, JOINTS
MULTI-BODY SIMULATIONS
The task of this assignment is to design a linkage mechanism that has one (1) degree of freedom that is able to position a plotter's pen on a flat, horizontal surface (such as a piece of paper on a table). The mechanism has to move the pen from the paper to its cap to prevent the pen from drying out when not in use.
The following diagram is provided within the assignment from the professor. It depicts the two extreme positions of the pen when it is deployed and when it is stored in its cap 1 cm above the writing surface.
CONSTRAINTS, as stated in the assignment:
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The pen will write on a horizontal, flat surface that lies 1 cm below the mounting surface of the mechanism, as illustrated in the figure above. No part of the mechanism shall extend below this surface when the pen is in the stored position.
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The pen must be positioned vertically and with its tip pointing downwards at each of the two extreme positions, but it may be tilted during transitions between them.
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The mechanism will be actuated through a servo motor or a stepper motor from your class kit.
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The mechanism, including the mounting surface (grounded link) shall consist of one module, independent of the paper, that can be transported without compromising its operation. No loose parts, no permanent fixtures to a table or other surface.
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You are free to select the pen and cap for your project. A Sharpie marker or a felt tip pen are acceptable; a pencil is not.
Math illustrations
Math Illustrations is a software that enables its users to both geometrically create and constrain figures, lines, and points. Taking what's defined, the software allows lengths, angles, and various properties to be altered. For example, a basic motion can be added to a series of connected line segments and turn a drawing into a simple animation.
Due to the capabilities of Math Illustrations, I utilized this software to sketch up my initial mechanism. The assignment specifies that the pen only has to remain vertical in its extreme positions (when on the paper or in its cap). The assignment specifications allow for a mechanism of any design. To set up the drawing space within the application, I created two infinite lines spaced 1 cm (0.3937 inches) apart to represent the two surfaces. Additionally, I drew up a rectangle polygon to resemble the pen cap as a means to aid in the visualization. The pen cap is measured to be 2 inches in height and 0.5 inches in width, approximate measurements based on a Sharpie marker.
As a starting point, I've decided to build upon a four-bar mechanism. A four-bar mechanism is composed of a frame (grounded link), rocker (output link), crank (input link), coupler (intermediate link). To accommodate for the pen's positioning throughout its transition, the coupler was modified to connect to a right triangle linkage that stays as this shape while the crank moves the mechanism. The vertical side of the right triangle will serve as the placement for the pen. Therefore, the pen remains vertical throughout all points of movement.
In order to maintain the composure of a right triangle fixed to the coupler, both the crank and rocker have to be parallel and of the same length. Additionally, this constrains the frame link and coupler (bottom side of the right triangle) to be of the same length.
The screenshot below displays the annotated setup of the Math Illustrations sketch.
Note that the fixed link is not drawn explicitly. This is a common convention; the fixed link is implied by constraining the coordinate of either the crank or rocker and dimensioning the distance between the two side links. An angle is denoted from the crank to the mounting surface. In actuality, a motor will rotate the crank and will be analyzed in detail later. To animate this sketch, the angle is set from a minimum value to a maximum value that satisfies the pen's movement from cap to paper. This program projects 22º to 162º as a satisfactory displacement. This is summarized in the two videos shown below. Both videos show the same animation, but the first video displays the annotated sketch, whereas the second video displays a cleaner version of the skeleton mechanism.
Solidworks
The sketch from Math Illustrations provides initial inputs and dimensions that can now almost be brought to life by designing the components in Solidworks. Before I began any computer-aided design (CAD), I wanted to analyze the initial mechanism and ensure that it is of 1 degree of freedom.
In Solidworks, I created two links, one of 5 inches the other of 7 inches, a pen, and two links to resemble the hypotenuse and right side of the triangle. I set the material of all links to AISI 1020 as instructed per the assignment. For consistency, I set the material of the pen to plastic. Each link has a hole dimensioned 0.5 inches from its nearest end, which will serve as the placement of the joints in the assembly. The links were designed as rectangular bars for simplicity but could be altered in the future to be of a more tailored shape. The rectangular design was chosen to reflect how I intended to cut the strips of foam board for my prototype, as cutting straight lines with an Exacto knife proves to be most manageable. The photos below are examples of some of the created CAD parts. Note that the depth for each link was set to 0.1850 inches as that is the thickness of the foam board.
Each link was assembled with a hinge mechanical mate to adjoin the corresponding concentric holes and coincident surfaces. The right triangle component will be further referred to as the pen holder/handler. As its sole purpose is to position the pen to the mechanism, its links have no intended motion from their connecting joints. The handler moves as a whole unit.
MACHINE DESIGN
MOTION CONVERSION
MACHINE COMPONENTS
MOTOR SIZING
MOTION ANALYSIS & MOTOR SIZING
With a CAD assembly built, a motion analysis can be applied with the help of the Solidworks Motion add-in. This add-in transforms the lifeless structure into a moving mechanism when a motor is applied. Since this assembly moves as intended when dragged with the cursor, applying a motor should move the crank as intended.
The crank is rotated in a circular path as the motor is attached at the bottom end of the link. A powered motor transforms electrical energy into mechanical energy. This mechanical energy provides a torque that displaces an object a certain distance given a certain amount of force. If the movement is executed in 500 ms, stop-to-stop, the force needed to move the pen is minimized when acceleration is minimized. Since I will be using a Sharpie with my prototype, all calculations were made to reflect the movement of a Sharpie from cap to paper. The approximate mass of a Sharpie is 7.5 grams and based on the Math Illustration model, the Sharpie is displaced 13.1 - 14 inches. In the ideal circumstance that the crank moves in the intended range of 22º to 162º, the Sharpie only moves 13.1 inches. However, it is more realistic to plan for the motor to have an allowable 0º to 180º ranger of motion as the ideal circumstance does not account for the width of the links or any limiting factors, including friction and inertia. The following document reflects the step-by-step calculations and rationalizations that I came to when determining the specifications for such a motor.
REFERENCES:
As a result, I determined that a 7.5g mass that is moved 14 inches by a 7-inch lever arm needs a motor with a torque of 7.59 N⋅mm and a speed of 107.5 rpm. After reaching this conclusion, I went back into my Solidworks assembly and started my Motion Analysis study. I applied a motor to the crank and created a "Trace Path" from the Results and Plots. The following video displays the movement of the motor-driven mechanism within the Solidworks Motion Analysis study.
Given a specified motion, such as adding a motor to a system, an external input defines the movement about a point and removes 1 degree of freedom. Note that the Gruebler count displayed at the start calculated the mechanism to have 0 degrees of freedom. This is calculated for the entire assembly with the applied motor. For CAD, a mechanism with 0 indicates a "well-constrained mechanism in kinematic analysis" [see reference for "Mechanism Analysis" on page 5]. For the analysis, the software also determines any redundancies with the user-defined mates to which the program found 5. The solver automatically resolves these when completing the analysis, which is ok for simple mechanisms but not the best practice for complex mechanisms. Since my design is of a simple magnitude, I elected to leave my constraints as they were set.
REFERENCES:
THE PROTOTYPE
Creating the mechanism
A physical prototype must be constructed using materials provided from our class kit. The prototype mechanism is then powered by a servo motor, which is programmed and controlled using an Arduino UNO board.
MATERIALS.
The class kit provided us with the following build materials:
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Foam boards
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Exacto knife and cutting mat
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Gorilla Glue
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Brass fasteners
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Hole puncher
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Moldable plastic
Additionally,
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Calipers, to measure
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Arduino UNO Board and supporting circuit board equipment
CONSTRUCTION.
In total, I created 6 rectangular foam links: two 7-inch, two 5-inch,
one 5.6-inch, one 2.5-inch. Each link has a width of 0.5 inches.
For each link, I punched a hole 0.5 inches from both ends. I used a brass fastener to join the necessary links together.
The fixed link is held by a small foam structure that keeps the mechanism and said linkage grounded.
The servo motor is attached to the rightmost link (the crank) directly at the joint (the point of rotation). The following series of pictures and diagrams show the connection of the motor to the Arduino UNO, the breadboard connections, the circuit diagram, and the code used to program the motion.
The Pen & Paper
THE MOUNTING SURFACE
The mechanism has to be mounted 1 cm from the writing surface. In order to accommodate this and preserve materials, I chose to use a notebook as my elevated surface. The mechanism and pen cap will lie on top of the notebook during the run-throughs. The photo to the right shows the measurement of the notebook to be 10.96 mm or roughly 1.1 cm.
THE PEN CAP
Since a Sharpie cap has no flat top, I created a holder out of moldable plastic. The photo above shows the bottom of the holder; the black silhouette at the center is the bottom of the pen cap. Therefore, the holder provides a negligible elevation to the cap and merely serves as a means to keep it upright when the pen is not in it.
THE PEN
Both unfortunately and ironically, the Sharpie I used for the project came to be completely dried out. The photo to the right shows random scribbles and even the word "test" faintly written at the upper right corner of the notebook.
Since the marker is dried out, the series of videos featuring the prototype in motion shows faint or missable markings when the pen is positioned on the paper. In an attempt to make up for this, the tip of the marker was slightly moistened for the side view video. Once the marker reached the writing surface, it left a small, dampened mark.
In the future, I plan on getting a new Sharpie, but unfortunately, this dried-out Sharpie was attached to the 2.5-inch foam link by Gorilla Glue and tape (acting as a clamp in curing the glue).
